Problems to Ponder (May edition)

Welcome to this month’s edition of Problems to Ponder! Pose them in your classroom as a challenge, or try them out yourself. Have an interesting student (or teacher) solution? Send it to thevariable@smts.ca for publication in a future issue ofThe Variable,our monthly periodical.

The problems are meant to be discussed in teams – we encourage you to pose them as a challenge in your classroom or your math club!

Grade 7-8 Problem: Magic decimalsMath Challenge 2016

In a magic square, the sums of the numbers in the rows, columns and diagonals are all equal. Use a 4×4 grid to make a magic square for these numbers: 0.1, 0.2, 0.3, 0.4, … 1.4, 1.5, 1.6.

Grade 9-10 Problem: RemaindersMath Challenge 2016

a) What is the smallest positive integer that leaves a remainder of 1 when divided by 2, remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and so on up to a remainder of 9 when divided by 10?

b) Dr. Theta wants to divide his class into equal groups. When he tries to divide his students into 5 groups, there are 2 students remaining without a group. He then tries to divide the students into 7 groups, but this leaves 3 students without a group. When he tries to divide the students into 9 groups, there are 4 students remaining. What is the smallest possible number of students in Dr. Theta’s class?